Solved on Aug 16, 2023

1. Order 42,13,6,38-42, -13, 6, 38 from least to greatest: 4213638-42 \leq -13 \leq 6 \leq 38. 2. Order 612,512,4,6-6 \frac{1}{2}, -5 \frac{1}{2}, -4, -6 from least to greatest: 61265124-6 \frac{1}{2} \leq -6 \leq -5 \frac{1}{2} \leq -4. 3. Order 8.999,0,17.56,823-8.999, 0, 17.56, -8 \frac{2}{3} from least to greatest: 8.999082317.56-8.999 \leq 0 \leq -8 \frac{2}{3} \leq 17.56. 4. Order 410,13,189,5-\frac{4}{10}, \frac{1}{3}, 1 \frac{8}{9}, -5 from least to greatest: 541013189-5 \leq -\frac{4}{10} \leq \frac{1}{3} \leq 1 \frac{8}{9}.

STEP 1

Assumptions1. The sets of numbers given are - Set1 38,42,13,638, -42, -13,6 - Set 51,4,61,6-5 \frac{1}{}, -4, -6 \frac{1}{}, -6 - Set3 17.56,83,0,8.99917.56, -8 \frac{}{3},0, -8.999 - Set4 13,410,189,5\frac{1}{3}, -\frac{4}{10},1 \frac{8}{9}, -5 . The task is to order each set of numbers from least to greatest.
3. The ordered sets should be written as inequality statements.

STEP 2

We start with the first set of numbers. The numbers are 38,42,13,638, -42, -13,6. We can see that 42-42 is the smallest number, followed by 13-13, then 66, and finally 3838 is the largest number.

STEP 3

Write the first set of numbers as an inequality statement from least to greatest.
4213638-42 \leq -13 \leq6 \leq38

STEP 4

Next, we move to the second set of numbers 12,4,612,6- \frac{1}{2}, -4, -6 \frac{1}{2}, -6. The smallest number is 612-6 \frac{1}{2}, followed by 6-6, then 12- \frac{1}{2}, and finally 4-4 is the largest number.

STEP 5

Write the second set of numbers as an inequality statement from least to greatest.
125124- \frac{1}{2} \leq - \leq -5 \frac{1}{2} \leq -4

STEP 6

Next, we move to the third set of numbers 17.56,823,0,8.99917.56, -8 \frac{2}{3},0, -8.999. The smallest number is 8.999-8.999, followed by 823-8 \frac{2}{3}, then 00, and finally 17.5617.56 is the largest number.

STEP 7

Write the third set of numbers as an inequality statement from least to greatest.
.99923017.56-.999 \leq - \frac{2}{3} \leq0 \leq17.56

STEP 8

Finally, we move to the fourth set of numbers 13,410,18,5\frac{1}{3}, -\frac{4}{10},1 \frac{8}{}, -5. The smallest number is 5-5, followed by 410-\frac{4}{10}, then 13\frac{1}{3}, and finally 181 \frac{8}{} is the largest number.

STEP 9

Write the fourth set of numbers as an inequality statement from least to greatest.
54389-5 \leq -\frac{4}{} \leq \frac{}{3} \leq \frac{8}{9}The ordered sets of numbers are. 4213638-42 \leq -13 \leq6 \leq38
2. 626524-6 \frac{}{2} \leq -6 \leq -5 \frac{}{2} \leq -4
3. 8.99982317.56-8.999 \leq -8 \frac{2}{3} \leq \leq17.56
4. 54389-5 \leq -\frac{4}{} \leq \frac{}{3} \leq \frac{8}{9}

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